Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D

Percentage Accurate: 99.5% → 99.8%

Time: 15.0s

Alternatives: 14

Speedup: 1.2×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - x, \mathsf{fma}\left(z, -6, 4\right), x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (- y x) (fma z -6.0 4.0) x))

C

double code(double x, double y, double z) {
	return fma((y - x), fma(z, -6.0, 4.0), x);
}

Julia

function code(x, y, z)
	return fma(Float64(y - x), fma(z, -6.0, 4.0), x)
end

Wolfram

code[x_, y_, z_] := N[(N[(y - x), $MachinePrecision] * N[(z * -6.0 + 4.0), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. +-commutative 99.6%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

   2. associate-*l* 99.8%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

   3. fma-define 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

   4. sub-neg 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

   5. +-commutative 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\left(-z\right) + \frac{2}{3}\right)}, x\right) \]

   6. distribute-lft-in 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{6 \cdot \left(-z\right) + 6 \cdot \frac{2}{3}}, x\right) \]

   7. distribute-rgt-neg-out 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(-6 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

   8. *-commutative 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \left(-\color{blue}{z \cdot 6}\right) + 6 \cdot \frac{2}{3}, x\right) \]

   9. distribute-rgt-neg-in 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(-6\right)} + 6 \cdot \frac{2}{3}, x\right) \]

   10. fma-define 99.8%

       \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, -6, 6 \cdot \frac{2}{3}\right)}, x\right) \]

   11. metadata-eval 99.8%

       \[\leadsto \mathsf{fma}\left(y - x, \mathsf{fma}\left(z, \color{blue}{-6}, 6 \cdot \frac{2}{3}\right), x\right) \]

   12. metadata-eval 99.8%

       \[\leadsto \mathsf{fma}\left(y - x, \mathsf{fma}\left(z, -6, 6 \cdot \color{blue}{0.6666666666666666}\right), x\right) \]

   13. metadata-eval 99.8%

       \[\leadsto \mathsf{fma}\left(y - x, \mathsf{fma}\left(z, -6, \color{blue}{4}\right), x\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \mathsf{fma}\left(z, -6, 4\right), x\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 99.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (- y x) (+ 4.0 (* z -6.0)) x))

C

double code(double x, double y, double z) {
	return fma((y - x), (4.0 + (z * -6.0)), x);
}

Julia

function code(x, y, z)
	return fma(Float64(y - x), Float64(4.0 + Float64(z * -6.0)), x)
end

Wolfram

code[x_, y_, z_] := N[(N[(y - x), $MachinePrecision] * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. +-commutative 99.6%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

   2. associate-*l* 99.8%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

   3. fma-define 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

   4. sub-neg 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

   5. distribute-rgt-in 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

   6. metadata-eval 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

   7. metadata-eval 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

   8. distribute-lft-neg-out 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

   9. distribute-rgt-neg-in 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

   10. metadata-eval 99.8%

       \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 3: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -210000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.15 \cdot 10^{-65}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-63}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+26}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -3.0 (* z 6.0)))) (t_1 (* -6.0 (* (- y x) z))))
   (if (<= z -210000000000.0)
     t_1
     (if (<= z -3.15e-65)
       t_0
       (if (<= z 6.2e-63) (* y 4.0) (if (<= z 1.25e+26) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -210000000000.0) {
		tmp = t_1;
	} else if (z <= -3.15e-65) {
		tmp = t_0;
	} else if (z <= 6.2e-63) {
		tmp = y * 4.0;
	} else if (z <= 1.25e+26) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * ((-3.0d0) + (z * 6.0d0))
    t_1 = (-6.0d0) * ((y - x) * z)
    if (z <= (-210000000000.0d0)) then
        tmp = t_1
    else if (z <= (-3.15d-65)) then
        tmp = t_0
    else if (z <= 6.2d-63) then
        tmp = y * 4.0d0
    else if (z <= 1.25d+26) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -210000000000.0) {
		tmp = t_1;
	} else if (z <= -3.15e-65) {
		tmp = t_0;
	} else if (z <= 6.2e-63) {
		tmp = y * 4.0;
	} else if (z <= 1.25e+26) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-3.0 + (z * 6.0))
	t_1 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -210000000000.0:
		tmp = t_1
	elif z <= -3.15e-65:
		tmp = t_0
	elif z <= 6.2e-63:
		tmp = y * 4.0
	elif z <= 1.25e+26:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	t_1 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -210000000000.0)
		tmp = t_1;
	elseif (z <= -3.15e-65)
		tmp = t_0;
	elseif (z <= 6.2e-63)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.25e+26)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-3.0 + (z * 6.0));
	t_1 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -210000000000.0)
		tmp = t_1;
	elseif (z <= -3.15e-65)
		tmp = t_0;
	elseif (z <= 6.2e-63)
		tmp = y * 4.0;
	elseif (z <= 1.25e+26)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -210000000000.0], t$95$1, If[LessEqual[z, -3.15e-65], t$95$0, If[LessEqual[z, 6.2e-63], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.25e+26], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1e11 or 1.25e26 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cube-cbrt 99.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) \]

      2. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)} \]

      3. pow2 99.8%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}, \sqrt[3]{x}, \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \]

      4. associate-*l* 99.8%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}\right) \]

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)} \]

   7. Taylor expanded in z around inf 99.7%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   if -2.1e11 < z < -3.1499999999999998e-65 or 6.19999999999999968e-63 < z < 1.25e26

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.4%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.4%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.4%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.7%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 75.3%

      \[\leadsto \color{blue}{x + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 75.3%

         \[\leadsto \color{blue}{1 \cdot x} + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right) \]

      2. *-commutative 75.3%

         \[\leadsto 1 \cdot x + -1 \cdot \color{blue}{\left(\left(4 + -6 \cdot z\right) \cdot x\right)} \]

      3. +-commutative 75.3%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\left(-6 \cdot z + 4\right)} \cdot x\right) \]

      4. *-commutative 75.3%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\left(\color{blue}{z \cdot -6} + 4\right) \cdot x\right) \]

      5. fma-define 75.3%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\mathsf{fma}\left(z, -6, 4\right)} \cdot x\right) \]

      6. associate-*r* 75.3%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \mathsf{fma}\left(z, -6, 4\right)\right) \cdot x} \]

      7. neg-mul-1 75.3%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-\mathsf{fma}\left(z, -6, 4\right)\right)} \cdot x \]

      8. fma-define 75.3%

         \[\leadsto 1 \cdot x + \left(-\color{blue}{\left(z \cdot -6 + 4\right)}\right) \cdot x \]

      9. distribute-neg-in 75.3%

         \[\leadsto 1 \cdot x + \color{blue}{\left(\left(-z \cdot -6\right) + \left(-4\right)\right)} \cdot x \]

      10. distribute-lft-neg-in 75.3%

          \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z\right) \cdot -6} + \left(-4\right)\right) \cdot x \]

      11. metadata-eval 75.3%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{-4}\right) \cdot x \]

      12. metadata-eval 75.3%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{0.6666666666666666 \cdot -6}\right) \cdot x \]

      13. distribute-rgt-in 75.2%

          \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(\left(-z\right) + 0.6666666666666666\right)\right)} \cdot x \]

      14. +-commutative 75.2%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      15. sub-neg 75.2%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 - z\right)}\right) \cdot x \]

      16. distribute-rgt-in 75.2%

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      17. sub-neg 75.2%

          \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      18. distribute-rgt-in 75.4%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      19. metadata-eval 75.4%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      20. distribute-lft-neg-in 75.4%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      21. associate-+r+ 75.4%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

   7. Simplified 75.4%

      \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

   if -3.1499999999999998e-65 < z < 6.19999999999999968e-63

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 93.4%

      \[\leadsto \color{blue}{y \cdot \left(-6 \cdot \frac{x \cdot \left(0.6666666666666666 - z\right)}{y} + \left(6 \cdot \left(0.6666666666666666 - z\right) + \frac{x}{y}\right)\right)} \]

   6. Taylor expanded in z around 0 93.4%

      \[\leadsto \color{blue}{y \cdot \left(4 + \left(-4 \cdot \frac{x}{y} + \frac{x}{y}\right)\right)} \]
   7. Step-by-step derivation

      1. distribute-lft1-in 93.8%

         \[\leadsto y \cdot \left(4 + \color{blue}{\left(-4 + 1\right) \cdot \frac{x}{y}}\right) \]

      2. metadata-eval 93.8%

         \[\leadsto y \cdot \left(4 + \color{blue}{-3} \cdot \frac{x}{y}\right) \]

   8. Simplified 93.8%

      \[\leadsto \color{blue}{y \cdot \left(4 + -3 \cdot \frac{x}{y}\right)} \]

   9. Taylor expanded in x around 0 66.6%

      \[\leadsto y \cdot \color{blue}{4} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -210000000000:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -3.15 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-63}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -210000000000:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 88000:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -210000000000.0)
   (* (- y x) (* z -6.0))
   (if (<= z -1.22e-65)
     (* x (+ -3.0 (* z 6.0)))
     (if (<= z 88000.0) (* y (+ 4.0 (* z -6.0))) (* z (* (- y x) -6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -210000000000.0) {
		tmp = (y - x) * (z * -6.0);
	} else if (z <= -1.22e-65) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 88000.0) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-210000000000.0d0)) then
        tmp = (y - x) * (z * (-6.0d0))
    else if (z <= (-1.22d-65)) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else if (z <= 88000.0d0) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    else
        tmp = z * ((y - x) * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -210000000000.0) {
		tmp = (y - x) * (z * -6.0);
	} else if (z <= -1.22e-65) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 88000.0) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -210000000000.0:
		tmp = (y - x) * (z * -6.0)
	elif z <= -1.22e-65:
		tmp = x * (-3.0 + (z * 6.0))
	elif z <= 88000.0:
		tmp = y * (4.0 + (z * -6.0))
	else:
		tmp = z * ((y - x) * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -210000000000.0)
		tmp = Float64(Float64(y - x) * Float64(z * -6.0));
	elseif (z <= -1.22e-65)
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	elseif (z <= 88000.0)
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	else
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -210000000000.0)
		tmp = (y - x) * (z * -6.0);
	elseif (z <= -1.22e-65)
		tmp = x * (-3.0 + (z * 6.0));
	elseif (z <= 88000.0)
		tmp = y * (4.0 + (z * -6.0));
	else
		tmp = z * ((y - x) * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -210000000000.0], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.22e-65], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 88000.0], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.1e11

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.9%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.8%

      \[\leadsto \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right) + \left(4 \cdot \frac{y - x}{z} + \frac{x}{z}\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto z \cdot \left(-6 \cdot \left(y - x\right) + \color{blue}{\left(\frac{x}{z} + 4 \cdot \frac{y - x}{z}\right)}\right) \]

      2. clear-num 99.8%

         \[\leadsto z \cdot \left(-6 \cdot \left(y - x\right) + \left(\color{blue}{\frac{1}{\frac{z}{x}}} + 4 \cdot \frac{y - x}{z}\right)\right) \]

      3. associate-*r/ 99.8%

         \[\leadsto z \cdot \left(-6 \cdot \left(y - x\right) + \left(\frac{1}{\frac{z}{x}} + \color{blue}{\frac{4 \cdot \left(y - x\right)}{z}}\right)\right) \]

      4. frac-add 67.1%

         \[\leadsto z \cdot \left(-6 \cdot \left(y - x\right) + \color{blue}{\frac{1 \cdot z + \frac{z}{x} \cdot \left(4 \cdot \left(y - x\right)\right)}{\frac{z}{x} \cdot z}}\right) \]

      5. *-un-lft-identity 67.1%

         \[\leadsto z \cdot \left(-6 \cdot \left(y - x\right) + \frac{\color{blue}{z} + \frac{z}{x} \cdot \left(4 \cdot \left(y - x\right)\right)}{\frac{z}{x} \cdot z}\right) \]

   7. Applied egg-rr 67.1%

      \[\leadsto z \cdot \left(-6 \cdot \left(y - x\right) + \color{blue}{\frac{z + \frac{z}{x} \cdot \left(4 \cdot \left(y - x\right)\right)}{\frac{z}{x} \cdot z}}\right) \]

   8. Taylor expanded in z around inf 99.7%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 99.9%

         \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 99.9%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(-6 \cdot z\right)} \]

      3. *-commutative 99.9%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\left(z \cdot -6\right)} \]

   10. Simplified 99.9%

       \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot -6\right)} \]

   if -2.1e11 < z < -1.21999999999999999e-65

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.4%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.7%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 87.6%

      \[\leadsto \color{blue}{x + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 87.6%

         \[\leadsto \color{blue}{1 \cdot x} + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right) \]

      2. *-commutative 87.6%

         \[\leadsto 1 \cdot x + -1 \cdot \color{blue}{\left(\left(4 + -6 \cdot z\right) \cdot x\right)} \]

      3. +-commutative 87.6%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\left(-6 \cdot z + 4\right)} \cdot x\right) \]

      4. *-commutative 87.6%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\left(\color{blue}{z \cdot -6} + 4\right) \cdot x\right) \]

      5. fma-define 87.6%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\mathsf{fma}\left(z, -6, 4\right)} \cdot x\right) \]

      6. associate-*r* 87.6%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \mathsf{fma}\left(z, -6, 4\right)\right) \cdot x} \]

      7. neg-mul-1 87.6%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-\mathsf{fma}\left(z, -6, 4\right)\right)} \cdot x \]

      8. fma-define 87.6%

         \[\leadsto 1 \cdot x + \left(-\color{blue}{\left(z \cdot -6 + 4\right)}\right) \cdot x \]

      9. distribute-neg-in 87.6%

         \[\leadsto 1 \cdot x + \color{blue}{\left(\left(-z \cdot -6\right) + \left(-4\right)\right)} \cdot x \]

      10. distribute-lft-neg-in 87.6%

          \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z\right) \cdot -6} + \left(-4\right)\right) \cdot x \]

      11. metadata-eval 87.6%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{-4}\right) \cdot x \]

      12. metadata-eval 87.6%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{0.6666666666666666 \cdot -6}\right) \cdot x \]

      13. distribute-rgt-in 87.5%

          \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(\left(-z\right) + 0.6666666666666666\right)\right)} \cdot x \]

      14. +-commutative 87.5%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      15. sub-neg 87.5%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 - z\right)}\right) \cdot x \]

      16. distribute-rgt-in 87.5%

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      17. sub-neg 87.5%

          \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      18. distribute-rgt-in 87.6%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      19. metadata-eval 87.6%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      20. distribute-lft-neg-in 87.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      21. associate-+r+ 87.6%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

   7. Simplified 87.6%

      \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

   if -1.21999999999999999e-65 < z < 88000

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.4%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 63.3%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]

   if 88000 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.8%

      \[\leadsto \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right) + \left(4 \cdot \frac{y - x}{z} + \frac{x}{z}\right)\right)} \]

   6. Taylor expanded in z around inf 98.5%

      \[\leadsto z \cdot \color{blue}{\left(-6 \cdot \left(y - x\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -210000000000:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 88000:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{if}\;z \leq -210000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 4100000:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* (- y x) -6.0))))
   (if (<= z -210000000000.0)
     t_0
     (if (<= z -1.6e-65)
       (* x (+ -3.0 (* z 6.0)))
       (if (<= z 4100000.0) (* y (+ 4.0 (* z -6.0))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -210000000000.0) {
		tmp = t_0;
	} else if (z <= -1.6e-65) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 4100000.0) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * ((y - x) * (-6.0d0))
    if (z <= (-210000000000.0d0)) then
        tmp = t_0
    else if (z <= (-1.6d-65)) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else if (z <= 4100000.0d0) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -210000000000.0) {
		tmp = t_0;
	} else if (z <= -1.6e-65) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 4100000.0) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * ((y - x) * -6.0)
	tmp = 0
	if z <= -210000000000.0:
		tmp = t_0
	elif z <= -1.6e-65:
		tmp = x * (-3.0 + (z * 6.0))
	elif z <= 4100000.0:
		tmp = y * (4.0 + (z * -6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(Float64(y - x) * -6.0))
	tmp = 0.0
	if (z <= -210000000000.0)
		tmp = t_0;
	elseif (z <= -1.6e-65)
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	elseif (z <= 4100000.0)
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * ((y - x) * -6.0);
	tmp = 0.0;
	if (z <= -210000000000.0)
		tmp = t_0;
	elseif (z <= -1.6e-65)
		tmp = x * (-3.0 + (z * 6.0));
	elseif (z <= 4100000.0)
		tmp = y * (4.0 + (z * -6.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -210000000000.0], t$95$0, If[LessEqual[z, -1.6e-65], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4100000.0], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1e11 or 4.1e6 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.8%

      \[\leadsto \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right) + \left(4 \cdot \frac{y - x}{z} + \frac{x}{z}\right)\right)} \]

   6. Taylor expanded in z around inf 99.2%

      \[\leadsto z \cdot \color{blue}{\left(-6 \cdot \left(y - x\right)\right)} \]

   if -2.1e11 < z < -1.6e-65

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.4%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.7%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 87.6%

      \[\leadsto \color{blue}{x + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 87.6%

         \[\leadsto \color{blue}{1 \cdot x} + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right) \]

      2. *-commutative 87.6%

         \[\leadsto 1 \cdot x + -1 \cdot \color{blue}{\left(\left(4 + -6 \cdot z\right) \cdot x\right)} \]

      3. +-commutative 87.6%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\left(-6 \cdot z + 4\right)} \cdot x\right) \]

      4. *-commutative 87.6%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\left(\color{blue}{z \cdot -6} + 4\right) \cdot x\right) \]

      5. fma-define 87.6%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\mathsf{fma}\left(z, -6, 4\right)} \cdot x\right) \]

      6. associate-*r* 87.6%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \mathsf{fma}\left(z, -6, 4\right)\right) \cdot x} \]

      7. neg-mul-1 87.6%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-\mathsf{fma}\left(z, -6, 4\right)\right)} \cdot x \]

      8. fma-define 87.6%

         \[\leadsto 1 \cdot x + \left(-\color{blue}{\left(z \cdot -6 + 4\right)}\right) \cdot x \]

      9. distribute-neg-in 87.6%

         \[\leadsto 1 \cdot x + \color{blue}{\left(\left(-z \cdot -6\right) + \left(-4\right)\right)} \cdot x \]

      10. distribute-lft-neg-in 87.6%

          \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z\right) \cdot -6} + \left(-4\right)\right) \cdot x \]

      11. metadata-eval 87.6%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{-4}\right) \cdot x \]

      12. metadata-eval 87.6%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{0.6666666666666666 \cdot -6}\right) \cdot x \]

      13. distribute-rgt-in 87.5%

          \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(\left(-z\right) + 0.6666666666666666\right)\right)} \cdot x \]

      14. +-commutative 87.5%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      15. sub-neg 87.5%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 - z\right)}\right) \cdot x \]

      16. distribute-rgt-in 87.5%

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      17. sub-neg 87.5%

          \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      18. distribute-rgt-in 87.6%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      19. metadata-eval 87.6%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      20. distribute-lft-neg-in 87.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      21. associate-+r+ 87.6%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

   7. Simplified 87.6%

      \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

   if -1.6e-65 < z < 4.1e6

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.4%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 63.3%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -210000000000:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 4100000:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -210000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 1260000:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -210000000000.0)
     t_0
     (if (<= z -8.8e-66)
       (* x (+ -3.0 (* z 6.0)))
       (if (<= z 1260000.0) (* y (+ 4.0 (* z -6.0))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -210000000000.0) {
		tmp = t_0;
	} else if (z <= -8.8e-66) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 1260000.0) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    if (z <= (-210000000000.0d0)) then
        tmp = t_0
    else if (z <= (-8.8d-66)) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else if (z <= 1260000.0d0) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -210000000000.0) {
		tmp = t_0;
	} else if (z <= -8.8e-66) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 1260000.0) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -210000000000.0:
		tmp = t_0
	elif z <= -8.8e-66:
		tmp = x * (-3.0 + (z * 6.0))
	elif z <= 1260000.0:
		tmp = y * (4.0 + (z * -6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -210000000000.0)
		tmp = t_0;
	elseif (z <= -8.8e-66)
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	elseif (z <= 1260000.0)
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -210000000000.0)
		tmp = t_0;
	elseif (z <= -8.8e-66)
		tmp = x * (-3.0 + (z * 6.0));
	elseif (z <= 1260000.0)
		tmp = y * (4.0 + (z * -6.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -210000000000.0], t$95$0, If[LessEqual[z, -8.8e-66], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1260000.0], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1e11 or 1.26e6 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cube-cbrt 99.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) \]

      2. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)} \]

      3. pow2 99.8%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}, \sqrt[3]{x}, \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \]

      4. associate-*l* 99.8%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}\right) \]

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)} \]

   7. Taylor expanded in z around inf 99.1%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   if -2.1e11 < z < -8.8000000000000004e-66

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.4%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.7%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 87.6%

      \[\leadsto \color{blue}{x + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 87.6%

         \[\leadsto \color{blue}{1 \cdot x} + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right) \]

      2. *-commutative 87.6%

         \[\leadsto 1 \cdot x + -1 \cdot \color{blue}{\left(\left(4 + -6 \cdot z\right) \cdot x\right)} \]

      3. +-commutative 87.6%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\left(-6 \cdot z + 4\right)} \cdot x\right) \]

      4. *-commutative 87.6%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\left(\color{blue}{z \cdot -6} + 4\right) \cdot x\right) \]

      5. fma-define 87.6%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\mathsf{fma}\left(z, -6, 4\right)} \cdot x\right) \]

      6. associate-*r* 87.6%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \mathsf{fma}\left(z, -6, 4\right)\right) \cdot x} \]

      7. neg-mul-1 87.6%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-\mathsf{fma}\left(z, -6, 4\right)\right)} \cdot x \]

      8. fma-define 87.6%

         \[\leadsto 1 \cdot x + \left(-\color{blue}{\left(z \cdot -6 + 4\right)}\right) \cdot x \]

      9. distribute-neg-in 87.6%

         \[\leadsto 1 \cdot x + \color{blue}{\left(\left(-z \cdot -6\right) + \left(-4\right)\right)} \cdot x \]

      10. distribute-lft-neg-in 87.6%

          \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z\right) \cdot -6} + \left(-4\right)\right) \cdot x \]

      11. metadata-eval 87.6%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{-4}\right) \cdot x \]

      12. metadata-eval 87.6%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{0.6666666666666666 \cdot -6}\right) \cdot x \]

      13. distribute-rgt-in 87.5%

          \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(\left(-z\right) + 0.6666666666666666\right)\right)} \cdot x \]

      14. +-commutative 87.5%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      15. sub-neg 87.5%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 - z\right)}\right) \cdot x \]

      16. distribute-rgt-in 87.5%

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      17. sub-neg 87.5%

          \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      18. distribute-rgt-in 87.6%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      19. metadata-eval 87.6%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      20. distribute-lft-neg-in 87.6%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      21. associate-+r+ 87.6%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

   7. Simplified 87.6%

      \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

   if -8.8000000000000004e-66 < z < 1.26e6

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.4%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 63.3%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -210000000000:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 1260000:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.044:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-66}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.63:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.044)
     t_0
     (if (<= z -7e-66) (* x -3.0) (if (<= z 0.63) (* y 4.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.044) {
		tmp = t_0;
	} else if (z <= -7e-66) {
		tmp = x * -3.0;
	} else if (z <= 0.63) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.044d0)) then
        tmp = t_0
    else if (z <= (-7d-66)) then
        tmp = x * (-3.0d0)
    else if (z <= 0.63d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.044) {
		tmp = t_0;
	} else if (z <= -7e-66) {
		tmp = x * -3.0;
	} else if (z <= 0.63) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.044:
		tmp = t_0
	elif z <= -7e-66:
		tmp = x * -3.0
	elif z <= 0.63:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.044)
		tmp = t_0;
	elseif (z <= -7e-66)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.63)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.044)
		tmp = t_0;
	elseif (z <= -7e-66)
		tmp = x * -3.0;
	elseif (z <= 0.63)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.044], t$95$0, If[LessEqual[z, -7e-66], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.63], N[(y * 4.0), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.043999999999999997 or 0.630000000000000004 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cube-cbrt 99.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) \]

      2. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)} \]

      3. pow2 99.8%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}, \sqrt[3]{x}, \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \]

      4. associate-*l* 99.8%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}\right) \]

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)} \]

   7. Taylor expanded in z around inf 97.2%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   if -0.043999999999999997 < z < -7.0000000000000001e-66

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.4%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.6%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.6%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.6%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.6%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.6%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.6%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.6%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 85.4%

      \[\leadsto \color{blue}{x + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 85.4%

         \[\leadsto \color{blue}{1 \cdot x} + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right) \]

      2. *-commutative 85.4%

         \[\leadsto 1 \cdot x + -1 \cdot \color{blue}{\left(\left(4 + -6 \cdot z\right) \cdot x\right)} \]

      3. +-commutative 85.4%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\left(-6 \cdot z + 4\right)} \cdot x\right) \]

      4. *-commutative 85.4%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\left(\color{blue}{z \cdot -6} + 4\right) \cdot x\right) \]

      5. fma-define 85.4%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\mathsf{fma}\left(z, -6, 4\right)} \cdot x\right) \]

      6. associate-*r* 85.4%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \mathsf{fma}\left(z, -6, 4\right)\right) \cdot x} \]

      7. neg-mul-1 85.4%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-\mathsf{fma}\left(z, -6, 4\right)\right)} \cdot x \]

      8. fma-define 85.4%

         \[\leadsto 1 \cdot x + \left(-\color{blue}{\left(z \cdot -6 + 4\right)}\right) \cdot x \]

      9. distribute-neg-in 85.4%

         \[\leadsto 1 \cdot x + \color{blue}{\left(\left(-z \cdot -6\right) + \left(-4\right)\right)} \cdot x \]

      10. distribute-lft-neg-in 85.4%

          \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z\right) \cdot -6} + \left(-4\right)\right) \cdot x \]

      11. metadata-eval 85.4%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{-4}\right) \cdot x \]

      12. metadata-eval 85.4%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{0.6666666666666666 \cdot -6}\right) \cdot x \]

      13. distribute-rgt-in 85.3%

          \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(\left(-z\right) + 0.6666666666666666\right)\right)} \cdot x \]

      14. +-commutative 85.3%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      15. sub-neg 85.3%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 - z\right)}\right) \cdot x \]

      16. distribute-rgt-in 85.2%

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      17. sub-neg 85.2%

          \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      18. distribute-rgt-in 85.3%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      19. metadata-eval 85.3%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      20. distribute-lft-neg-in 85.3%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      21. associate-+r+ 85.3%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

   7. Simplified 85.3%

      \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

   8. Taylor expanded in z around 0 82.1%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 82.1%

         \[\leadsto \color{blue}{x \cdot -3} \]

   10. Simplified 82.1%

       \[\leadsto \color{blue}{x \cdot -3} \]

   if -7.0000000000000001e-66 < z < 0.630000000000000004

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 92.4%

      \[\leadsto \color{blue}{y \cdot \left(-6 \cdot \frac{x \cdot \left(0.6666666666666666 - z\right)}{y} + \left(6 \cdot \left(0.6666666666666666 - z\right) + \frac{x}{y}\right)\right)} \]

   6. Taylor expanded in z around 0 90.5%

      \[\leadsto \color{blue}{y \cdot \left(4 + \left(-4 \cdot \frac{x}{y} + \frac{x}{y}\right)\right)} \]
   7. Step-by-step derivation

      1. distribute-lft1-in 91.0%

         \[\leadsto y \cdot \left(4 + \color{blue}{\left(-4 + 1\right) \cdot \frac{x}{y}}\right) \]

      2. metadata-eval 91.0%

         \[\leadsto y \cdot \left(4 + \color{blue}{-3} \cdot \frac{x}{y}\right) \]

   8. Simplified 91.0%

      \[\leadsto \color{blue}{y \cdot \left(4 + -3 \cdot \frac{x}{y}\right)} \]

   9. Taylor expanded in x around 0 62.0%

      \[\leadsto y \cdot \color{blue}{4} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.044:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-66}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.63:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-65}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.54:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z 6.0))))
   (if (<= z -0.5)
     t_0
     (if (<= z -4.2e-65) (* x -3.0) (if (<= z 0.54) (* y 4.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= -4.2e-65) {
		tmp = x * -3.0;
	} else if (z <= 0.54) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (z * 6.0d0)
    if (z <= (-0.5d0)) then
        tmp = t_0
    else if (z <= (-4.2d-65)) then
        tmp = x * (-3.0d0)
    else if (z <= 0.54d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= -4.2e-65) {
		tmp = x * -3.0;
	} else if (z <= 0.54) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * 6.0)
	tmp = 0
	if z <= -0.5:
		tmp = t_0
	elif z <= -4.2e-65:
		tmp = x * -3.0
	elif z <= 0.54:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -0.5)
		tmp = t_0;
	elseif (z <= -4.2e-65)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.54)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -0.5)
		tmp = t_0;
	elseif (z <= -4.2e-65)
		tmp = x * -3.0;
	elseif (z <= 0.54)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.5], t$95$0, If[LessEqual[z, -4.2e-65], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.54], N[(y * 4.0), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.5 or 0.54000000000000004 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 60.0%

      \[\leadsto \color{blue}{x + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 60.0%

         \[\leadsto \color{blue}{1 \cdot x} + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right) \]

      2. *-commutative 60.0%

         \[\leadsto 1 \cdot x + -1 \cdot \color{blue}{\left(\left(4 + -6 \cdot z\right) \cdot x\right)} \]

      3. +-commutative 60.0%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\left(-6 \cdot z + 4\right)} \cdot x\right) \]

      4. *-commutative 60.0%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\left(\color{blue}{z \cdot -6} + 4\right) \cdot x\right) \]

      5. fma-define 60.0%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\mathsf{fma}\left(z, -6, 4\right)} \cdot x\right) \]

      6. associate-*r* 60.0%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \mathsf{fma}\left(z, -6, 4\right)\right) \cdot x} \]

      7. neg-mul-1 60.0%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-\mathsf{fma}\left(z, -6, 4\right)\right)} \cdot x \]

      8. fma-define 60.0%

         \[\leadsto 1 \cdot x + \left(-\color{blue}{\left(z \cdot -6 + 4\right)}\right) \cdot x \]

      9. distribute-neg-in 60.0%

         \[\leadsto 1 \cdot x + \color{blue}{\left(\left(-z \cdot -6\right) + \left(-4\right)\right)} \cdot x \]

      10. distribute-lft-neg-in 60.0%

          \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z\right) \cdot -6} + \left(-4\right)\right) \cdot x \]

      11. metadata-eval 60.0%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{-4}\right) \cdot x \]

      12. metadata-eval 60.0%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{0.6666666666666666 \cdot -6}\right) \cdot x \]

      13. distribute-rgt-in 60.0%

          \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(\left(-z\right) + 0.6666666666666666\right)\right)} \cdot x \]

      14. +-commutative 60.0%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      15. sub-neg 60.0%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 - z\right)}\right) \cdot x \]

      16. distribute-rgt-in 60.0%

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      17. sub-neg 60.0%

          \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      18. distribute-rgt-in 60.0%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      19. metadata-eval 60.0%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      20. distribute-lft-neg-in 60.0%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      21. associate-+r+ 60.0%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

   7. Simplified 60.0%

      \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

   8. Taylor expanded in z around inf 57.9%

      \[\leadsto \color{blue}{6 \cdot \left(x \cdot z\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 57.9%

         \[\leadsto \color{blue}{\left(6 \cdot x\right) \cdot z} \]

      2. *-commutative 57.9%

         \[\leadsto \color{blue}{\left(x \cdot 6\right)} \cdot z \]

      3. associate-*r* 57.9%

         \[\leadsto \color{blue}{x \cdot \left(6 \cdot z\right)} \]

   10. Simplified 57.9%

       \[\leadsto \color{blue}{x \cdot \left(6 \cdot z\right)} \]

   if -0.5 < z < -4.20000000000000006e-65

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.4%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.6%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.6%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.6%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.6%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.6%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.6%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.6%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 85.4%

      \[\leadsto \color{blue}{x + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 85.4%

         \[\leadsto \color{blue}{1 \cdot x} + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right) \]

      2. *-commutative 85.4%

         \[\leadsto 1 \cdot x + -1 \cdot \color{blue}{\left(\left(4 + -6 \cdot z\right) \cdot x\right)} \]

      3. +-commutative 85.4%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\left(-6 \cdot z + 4\right)} \cdot x\right) \]

      4. *-commutative 85.4%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\left(\color{blue}{z \cdot -6} + 4\right) \cdot x\right) \]

      5. fma-define 85.4%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\mathsf{fma}\left(z, -6, 4\right)} \cdot x\right) \]

      6. associate-*r* 85.4%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \mathsf{fma}\left(z, -6, 4\right)\right) \cdot x} \]

      7. neg-mul-1 85.4%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-\mathsf{fma}\left(z, -6, 4\right)\right)} \cdot x \]

      8. fma-define 85.4%

         \[\leadsto 1 \cdot x + \left(-\color{blue}{\left(z \cdot -6 + 4\right)}\right) \cdot x \]

      9. distribute-neg-in 85.4%

         \[\leadsto 1 \cdot x + \color{blue}{\left(\left(-z \cdot -6\right) + \left(-4\right)\right)} \cdot x \]

      10. distribute-lft-neg-in 85.4%

          \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z\right) \cdot -6} + \left(-4\right)\right) \cdot x \]

      11. metadata-eval 85.4%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{-4}\right) \cdot x \]

      12. metadata-eval 85.4%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{0.6666666666666666 \cdot -6}\right) \cdot x \]

      13. distribute-rgt-in 85.3%

          \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(\left(-z\right) + 0.6666666666666666\right)\right)} \cdot x \]

      14. +-commutative 85.3%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      15. sub-neg 85.3%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 - z\right)}\right) \cdot x \]

      16. distribute-rgt-in 85.2%

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      17. sub-neg 85.2%

          \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      18. distribute-rgt-in 85.3%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      19. metadata-eval 85.3%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      20. distribute-lft-neg-in 85.3%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      21. associate-+r+ 85.3%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

   7. Simplified 85.3%

      \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

   8. Taylor expanded in z around 0 82.1%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 82.1%

         \[\leadsto \color{blue}{x \cdot -3} \]

   10. Simplified 82.1%

       \[\leadsto \color{blue}{x \cdot -3} \]

   if -4.20000000000000006e-65 < z < 0.54000000000000004

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 92.4%

      \[\leadsto \color{blue}{y \cdot \left(-6 \cdot \frac{x \cdot \left(0.6666666666666666 - z\right)}{y} + \left(6 \cdot \left(0.6666666666666666 - z\right) + \frac{x}{y}\right)\right)} \]

   6. Taylor expanded in z around 0 90.5%

      \[\leadsto \color{blue}{y \cdot \left(4 + \left(-4 \cdot \frac{x}{y} + \frac{x}{y}\right)\right)} \]
   7. Step-by-step derivation

      1. distribute-lft1-in 91.0%

         \[\leadsto y \cdot \left(4 + \color{blue}{\left(-4 + 1\right) \cdot \frac{x}{y}}\right) \]

      2. metadata-eval 91.0%

         \[\leadsto y \cdot \left(4 + \color{blue}{-3} \cdot \frac{x}{y}\right) \]

   8. Simplified 91.0%

      \[\leadsto \color{blue}{y \cdot \left(4 + -3 \cdot \frac{x}{y}\right)} \]

   9. Taylor expanded in x around 0 62.0%

      \[\leadsto y \cdot \color{blue}{4} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-65}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.54:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-66}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.63:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))))
   (if (<= z -0.5)
     t_0
     (if (<= z -6.5e-66) (* x -3.0) (if (<= z 0.63) (* y 4.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= -6.5e-66) {
		tmp = x * -3.0;
	} else if (z <= 0.63) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (x * z)
    if (z <= (-0.5d0)) then
        tmp = t_0
    else if (z <= (-6.5d-66)) then
        tmp = x * (-3.0d0)
    else if (z <= 0.63d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= -6.5e-66) {
		tmp = x * -3.0;
	} else if (z <= 0.63) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	tmp = 0
	if z <= -0.5:
		tmp = t_0
	elif z <= -6.5e-66:
		tmp = x * -3.0
	elif z <= 0.63:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -0.5)
		tmp = t_0;
	elseif (z <= -6.5e-66)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.63)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -0.5)
		tmp = t_0;
	elseif (z <= -6.5e-66)
		tmp = x * -3.0;
	elseif (z <= 0.63)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.5], t$95$0, If[LessEqual[z, -6.5e-66], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.63], N[(y * 4.0), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.5 or 0.630000000000000004 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 60.0%

      \[\leadsto \color{blue}{x + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 60.0%

         \[\leadsto \color{blue}{1 \cdot x} + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right) \]

      2. *-commutative 60.0%

         \[\leadsto 1 \cdot x + -1 \cdot \color{blue}{\left(\left(4 + -6 \cdot z\right) \cdot x\right)} \]

      3. +-commutative 60.0%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\left(-6 \cdot z + 4\right)} \cdot x\right) \]

      4. *-commutative 60.0%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\left(\color{blue}{z \cdot -6} + 4\right) \cdot x\right) \]

      5. fma-define 60.0%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\mathsf{fma}\left(z, -6, 4\right)} \cdot x\right) \]

      6. associate-*r* 60.0%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \mathsf{fma}\left(z, -6, 4\right)\right) \cdot x} \]

      7. neg-mul-1 60.0%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-\mathsf{fma}\left(z, -6, 4\right)\right)} \cdot x \]

      8. fma-define 60.0%

         \[\leadsto 1 \cdot x + \left(-\color{blue}{\left(z \cdot -6 + 4\right)}\right) \cdot x \]

      9. distribute-neg-in 60.0%

         \[\leadsto 1 \cdot x + \color{blue}{\left(\left(-z \cdot -6\right) + \left(-4\right)\right)} \cdot x \]

      10. distribute-lft-neg-in 60.0%

          \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z\right) \cdot -6} + \left(-4\right)\right) \cdot x \]

      11. metadata-eval 60.0%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{-4}\right) \cdot x \]

      12. metadata-eval 60.0%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{0.6666666666666666 \cdot -6}\right) \cdot x \]

      13. distribute-rgt-in 60.0%

          \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(\left(-z\right) + 0.6666666666666666\right)\right)} \cdot x \]

      14. +-commutative 60.0%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      15. sub-neg 60.0%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 - z\right)}\right) \cdot x \]

      16. distribute-rgt-in 60.0%

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      17. sub-neg 60.0%

          \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      18. distribute-rgt-in 60.0%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      19. metadata-eval 60.0%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      20. distribute-lft-neg-in 60.0%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      21. associate-+r+ 60.0%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

   7. Simplified 60.0%

      \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

   8. Taylor expanded in z around inf 57.9%

      \[\leadsto \color{blue}{6 \cdot \left(x \cdot z\right)} \]

   if -0.5 < z < -6.50000000000000024e-66

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.4%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.6%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.6%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.6%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.6%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.6%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.6%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.6%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 85.4%

      \[\leadsto \color{blue}{x + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 85.4%

         \[\leadsto \color{blue}{1 \cdot x} + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right) \]

      2. *-commutative 85.4%

         \[\leadsto 1 \cdot x + -1 \cdot \color{blue}{\left(\left(4 + -6 \cdot z\right) \cdot x\right)} \]

      3. +-commutative 85.4%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\left(-6 \cdot z + 4\right)} \cdot x\right) \]

      4. *-commutative 85.4%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\left(\color{blue}{z \cdot -6} + 4\right) \cdot x\right) \]

      5. fma-define 85.4%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\mathsf{fma}\left(z, -6, 4\right)} \cdot x\right) \]

      6. associate-*r* 85.4%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \mathsf{fma}\left(z, -6, 4\right)\right) \cdot x} \]

      7. neg-mul-1 85.4%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-\mathsf{fma}\left(z, -6, 4\right)\right)} \cdot x \]

      8. fma-define 85.4%

         \[\leadsto 1 \cdot x + \left(-\color{blue}{\left(z \cdot -6 + 4\right)}\right) \cdot x \]

      9. distribute-neg-in 85.4%

         \[\leadsto 1 \cdot x + \color{blue}{\left(\left(-z \cdot -6\right) + \left(-4\right)\right)} \cdot x \]

      10. distribute-lft-neg-in 85.4%

          \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z\right) \cdot -6} + \left(-4\right)\right) \cdot x \]

      11. metadata-eval 85.4%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{-4}\right) \cdot x \]

      12. metadata-eval 85.4%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{0.6666666666666666 \cdot -6}\right) \cdot x \]

      13. distribute-rgt-in 85.3%

          \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(\left(-z\right) + 0.6666666666666666\right)\right)} \cdot x \]

      14. +-commutative 85.3%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      15. sub-neg 85.3%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 - z\right)}\right) \cdot x \]

      16. distribute-rgt-in 85.2%

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      17. sub-neg 85.2%

          \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      18. distribute-rgt-in 85.3%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      19. metadata-eval 85.3%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      20. distribute-lft-neg-in 85.3%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      21. associate-+r+ 85.3%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

   7. Simplified 85.3%

      \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

   8. Taylor expanded in z around 0 82.1%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 82.1%

         \[\leadsto \color{blue}{x \cdot -3} \]

   10. Simplified 82.1%

       \[\leadsto \color{blue}{x \cdot -3} \]

   if -6.50000000000000024e-66 < z < 0.630000000000000004

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 92.4%

      \[\leadsto \color{blue}{y \cdot \left(-6 \cdot \frac{x \cdot \left(0.6666666666666666 - z\right)}{y} + \left(6 \cdot \left(0.6666666666666666 - z\right) + \frac{x}{y}\right)\right)} \]

   6. Taylor expanded in z around 0 90.5%

      \[\leadsto \color{blue}{y \cdot \left(4 + \left(-4 \cdot \frac{x}{y} + \frac{x}{y}\right)\right)} \]
   7. Step-by-step derivation

      1. distribute-lft1-in 91.0%

         \[\leadsto y \cdot \left(4 + \color{blue}{\left(-4 + 1\right) \cdot \frac{x}{y}}\right) \]

      2. metadata-eval 91.0%

         \[\leadsto y \cdot \left(4 + \color{blue}{-3} \cdot \frac{x}{y}\right) \]

   8. Simplified 91.0%

      \[\leadsto \color{blue}{y \cdot \left(4 + -3 \cdot \frac{x}{y}\right)} \]

   9. Taylor expanded in x around 0 62.0%

      \[\leadsto y \cdot \color{blue}{4} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 97.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.6)
   (* (- y x) (* z -6.0))
   (if (<= z 0.66) (+ x (* (- y x) 4.0)) (* z (* (- y x) -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.6) {
		tmp = (y - x) * (z * -6.0);
	} else if (z <= 0.66) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.6d0)) then
        tmp = (y - x) * (z * (-6.0d0))
    else if (z <= 0.66d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = z * ((y - x) * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.6) {
		tmp = (y - x) * (z * -6.0);
	} else if (z <= 0.66) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.6:
		tmp = (y - x) * (z * -6.0)
	elif z <= 0.66:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = z * ((y - x) * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.6)
		tmp = Float64(Float64(y - x) * Float64(z * -6.0));
	elseif (z <= 0.66)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.6)
		tmp = (y - x) * (z * -6.0);
	elseif (z <= 0.66)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = z * ((y - x) * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.6], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.66], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.599999999999999978

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.8%

      \[\leadsto \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right) + \left(4 \cdot \frac{y - x}{z} + \frac{x}{z}\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto z \cdot \left(-6 \cdot \left(y - x\right) + \color{blue}{\left(\frac{x}{z} + 4 \cdot \frac{y - x}{z}\right)}\right) \]

      2. clear-num 99.8%

         \[\leadsto z \cdot \left(-6 \cdot \left(y - x\right) + \left(\color{blue}{\frac{1}{\frac{z}{x}}} + 4 \cdot \frac{y - x}{z}\right)\right) \]

      3. associate-*r/ 99.8%

         \[\leadsto z \cdot \left(-6 \cdot \left(y - x\right) + \left(\frac{1}{\frac{z}{x}} + \color{blue}{\frac{4 \cdot \left(y - x\right)}{z}}\right)\right) \]

      4. frac-add 68.6%

         \[\leadsto z \cdot \left(-6 \cdot \left(y - x\right) + \color{blue}{\frac{1 \cdot z + \frac{z}{x} \cdot \left(4 \cdot \left(y - x\right)\right)}{\frac{z}{x} \cdot z}}\right) \]

      5. *-un-lft-identity 68.6%

         \[\leadsto z \cdot \left(-6 \cdot \left(y - x\right) + \frac{\color{blue}{z} + \frac{z}{x} \cdot \left(4 \cdot \left(y - x\right)\right)}{\frac{z}{x} \cdot z}\right) \]

   7. Applied egg-rr 68.6%

      \[\leadsto z \cdot \left(-6 \cdot \left(y - x\right) + \color{blue}{\frac{z + \frac{z}{x} \cdot \left(4 \cdot \left(y - x\right)\right)}{\frac{z}{x} \cdot z}}\right) \]

   8. Taylor expanded in z around inf 97.7%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 97.8%

         \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 97.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(-6 \cdot z\right)} \]

      3. *-commutative 97.8%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\left(z \cdot -6\right)} \]

   10. Simplified 97.8%

       \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot -6\right)} \]

   if -0.599999999999999978 < z < 0.660000000000000031

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 97.2%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   if 0.660000000000000031 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.7%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.8%

      \[\leadsto \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right) + \left(4 \cdot \frac{y - x}{z} + \frac{x}{z}\right)\right)} \]

   6. Taylor expanded in z around inf 96.8%

      \[\leadsto z \cdot \color{blue}{\left(-6 \cdot \left(y - x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-82} \lor \neg \left(x \leq 5.6 \cdot 10^{+17}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.05e-82) (not (<= x 5.6e+17))) (* x -3.0) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.05e-82) || !(x <= 5.6e+17)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.05d-82)) .or. (.not. (x <= 5.6d+17))) then
        tmp = x * (-3.0d0)
    else
        tmp = y * 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.05e-82) || !(x <= 5.6e+17)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.05e-82) or not (x <= 5.6e+17):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.05e-82) || !(x <= 5.6e+17))
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(y * 4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.05e-82) || ~((x <= 5.6e+17)))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.05e-82], N[Not[LessEqual[x, 5.6e+17]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05e-82 or 5.6e17 < x

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.6%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 80.5%

      \[\leadsto \color{blue}{x + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 80.5%

         \[\leadsto \color{blue}{1 \cdot x} + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right) \]

      2. *-commutative 80.5%

         \[\leadsto 1 \cdot x + -1 \cdot \color{blue}{\left(\left(4 + -6 \cdot z\right) \cdot x\right)} \]

      3. +-commutative 80.5%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\left(-6 \cdot z + 4\right)} \cdot x\right) \]

      4. *-commutative 80.5%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\left(\color{blue}{z \cdot -6} + 4\right) \cdot x\right) \]

      5. fma-define 80.4%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\mathsf{fma}\left(z, -6, 4\right)} \cdot x\right) \]

      6. associate-*r* 80.4%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \mathsf{fma}\left(z, -6, 4\right)\right) \cdot x} \]

      7. neg-mul-1 80.4%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-\mathsf{fma}\left(z, -6, 4\right)\right)} \cdot x \]

      8. fma-define 80.5%

         \[\leadsto 1 \cdot x + \left(-\color{blue}{\left(z \cdot -6 + 4\right)}\right) \cdot x \]

      9. distribute-neg-in 80.5%

         \[\leadsto 1 \cdot x + \color{blue}{\left(\left(-z \cdot -6\right) + \left(-4\right)\right)} \cdot x \]

      10. distribute-lft-neg-in 80.5%

          \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z\right) \cdot -6} + \left(-4\right)\right) \cdot x \]

      11. metadata-eval 80.5%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{-4}\right) \cdot x \]

      12. metadata-eval 80.5%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{0.6666666666666666 \cdot -6}\right) \cdot x \]

      13. distribute-rgt-in 80.4%

          \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(\left(-z\right) + 0.6666666666666666\right)\right)} \cdot x \]

      14. +-commutative 80.4%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      15. sub-neg 80.4%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 - z\right)}\right) \cdot x \]

      16. distribute-rgt-in 80.4%

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      17. sub-neg 80.4%

          \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      18. distribute-rgt-in 80.5%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      19. metadata-eval 80.5%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      20. distribute-lft-neg-in 80.5%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      21. associate-+r+ 80.5%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

   7. Simplified 80.5%

      \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

   8. Taylor expanded in z around 0 31.7%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 31.7%

         \[\leadsto \color{blue}{x \cdot -3} \]

   10. Simplified 31.7%

       \[\leadsto \color{blue}{x \cdot -3} \]

   if -1.05e-82 < x < 5.6e17

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.5%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 97.5%

      \[\leadsto \color{blue}{y \cdot \left(-6 \cdot \frac{x \cdot \left(0.6666666666666666 - z\right)}{y} + \left(6 \cdot \left(0.6666666666666666 - z\right) + \frac{x}{y}\right)\right)} \]

   6. Taylor expanded in z around 0 61.1%

      \[\leadsto \color{blue}{y \cdot \left(4 + \left(-4 \cdot \frac{x}{y} + \frac{x}{y}\right)\right)} \]
   7. Step-by-step derivation

      1. distribute-lft1-in 61.1%

         \[\leadsto y \cdot \left(4 + \color{blue}{\left(-4 + 1\right) \cdot \frac{x}{y}}\right) \]

      2. metadata-eval 61.1%

         \[\leadsto y \cdot \left(4 + \color{blue}{-3} \cdot \frac{x}{y}\right) \]

   8. Simplified 61.1%

      \[\leadsto \color{blue}{y \cdot \left(4 + -3 \cdot \frac{x}{y}\right)} \]

   9. Taylor expanded in x around 0 49.9%

      \[\leadsto y \cdot \color{blue}{4} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-82} \lor \neg \left(x \leq 5.6 \cdot 10^{+17}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- 0.6666666666666666 z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * (0.6666666666666666 - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * (0.6666666666666666d0 - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * (0.6666666666666666 - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * (0.6666666666666666 - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(0.6666666666666666 - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * (0.6666666666666666 - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.6%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 13: 26.3% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ x \cdot -3 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x -3.0))

C

double code(double x, double y, double z) {
	return x * -3.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (-3.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return x * -3.0;
}

Python

def code(x, y, z):
	return x * -3.0

Julia

function code(x, y, z)
	return Float64(x * -3.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * -3.0;
end

Wolfram

code[x_, y_, z_] := N[(x * -3.0), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. +-commutative 99.6%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

   2. associate-*l* 99.8%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

   3. fma-define 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

   4. sub-neg 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

   5. distribute-rgt-in 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

   6. metadata-eval 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

   7. metadata-eval 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

   8. distribute-lft-neg-out 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

   9. distribute-rgt-neg-in 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

   10. metadata-eval 99.8%

       \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 52.4%

   \[\leadsto \color{blue}{x + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right)} \]
6. Step-by-step derivation

   1. *-lft-identity 52.4%

      \[\leadsto \color{blue}{1 \cdot x} + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right) \]

   2. *-commutative 52.4%

      \[\leadsto 1 \cdot x + -1 \cdot \color{blue}{\left(\left(4 + -6 \cdot z\right) \cdot x\right)} \]

   3. +-commutative 52.4%

      \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\left(-6 \cdot z + 4\right)} \cdot x\right) \]

   4. *-commutative 52.4%

      \[\leadsto 1 \cdot x + -1 \cdot \left(\left(\color{blue}{z \cdot -6} + 4\right) \cdot x\right) \]

   5. fma-define 52.4%

      \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\mathsf{fma}\left(z, -6, 4\right)} \cdot x\right) \]

   6. associate-*r* 52.4%

      \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \mathsf{fma}\left(z, -6, 4\right)\right) \cdot x} \]

   7. neg-mul-1 52.4%

      \[\leadsto 1 \cdot x + \color{blue}{\left(-\mathsf{fma}\left(z, -6, 4\right)\right)} \cdot x \]

   8. fma-define 52.4%

      \[\leadsto 1 \cdot x + \left(-\color{blue}{\left(z \cdot -6 + 4\right)}\right) \cdot x \]

   9. distribute-neg-in 52.4%

      \[\leadsto 1 \cdot x + \color{blue}{\left(\left(-z \cdot -6\right) + \left(-4\right)\right)} \cdot x \]

   10. distribute-lft-neg-in 52.4%

       \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z\right) \cdot -6} + \left(-4\right)\right) \cdot x \]

   11. metadata-eval 52.4%

       \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{-4}\right) \cdot x \]

   12. metadata-eval 52.4%

       \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{0.6666666666666666 \cdot -6}\right) \cdot x \]

   13. distribute-rgt-in 52.3%

       \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(\left(-z\right) + 0.6666666666666666\right)\right)} \cdot x \]

   14. +-commutative 52.3%

       \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

   15. sub-neg 52.3%

       \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 - z\right)}\right) \cdot x \]

   16. distribute-rgt-in 52.3%

       \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

   17. sub-neg 52.3%

       \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

   18. distribute-rgt-in 52.4%

       \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

   19. metadata-eval 52.4%

       \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

   20. distribute-lft-neg-in 52.4%

       \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

   21. associate-+r+ 52.4%

       \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

7. Simplified 52.4%

   \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

8. Taylor expanded in z around 0 22.9%

   \[\leadsto \color{blue}{-3 \cdot x} \]
9. Step-by-step derivation

   1. *-commutative 22.9%

      \[\leadsto \color{blue}{x \cdot -3} \]

10. Simplified 22.9%

    \[\leadsto \color{blue}{x \cdot -3} \]
11. Add Preprocessing

Alternative 14: 2.6% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.6%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 50.6%

   \[\leadsto x + \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

6. Taylor expanded in z around 0 2.8%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024145 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))